• Industrial Engineering and Management Systems
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• v.15 no.2
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• pp.131-142
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• 2016

We consider a multi-server queueing system without buffer and with two types of customers as a model of operation of a mobile network cell. Customers arrive at the system in the marked Markovian arrival flow. The service times of customers are exponentially distributed with parameters depending on the type of customer. A part of the available servers is reserved exclusively for service of first type customers. Customers who do not receive service upon arrival, can make repeated attempts. The system operation is influenced by random factors, leading to a change of the system parameters, including the total number of servers and the number of reserved servers. The behavior of the system is described by the multi-dimensional Markov chain. The generator of this Markov chain is constructed and the ergodicity condition is derived. Formulas for computation of the main performance measures of the system based on the stationary distribution of the Markov chain are derived. Numerical examples are presented.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.2
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• pp.289-298
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• 1995

We consider a general queueing network with multi-server stations. The stations are under heavy traffics or moderate variable conditions. We develope an algorithm to determine the optimal loading policy, which minimizes the congestion in a network. Under more specified condition, majorization and arrangement orderings are established to compare, respectively, various loading and assignment policies. Implications of results are also discussed.

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.2
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• pp.168-174
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• 2000

All the visiting customers makes a queue and then can be served at an unoccupied server, in the queueing system of multi-server. The customer and server, however, have a conflictive feeling of satisfaction at all times. To solve the problem, in this paper, it is proposed that new design method of server number to maximize the satisfaction level of customer and server by the hzzy concept which is applied to the queuing system.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.601-616
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• 2021

Retrial queueing models have been studied extensively in the literature. These have many practical applications, especially in service sectors. However, retrial queueing models have their own limitations. Typically, analyzing such models involve level-dependent quasi-birth-and-death processes, and hence some form of a truncation or an approximate method or simulation approach is needed to study in steady-state. Secondly, in general, the customers are not served on a first-come-first-served basis. The latter is the case when a new arrival may find a free server while prior arrivals are waiting in the retrial orbit due to the servers being busy during their arrivals. In this paper, we take a different approach to the study of multi-server retrial queues in which the signals are generated in such a way to provide a reasonably fair treatment to all the customers seeking service. Further, this approach makes the study to be level-independent quasi-birth-and-death process. This approach is different from any considered in the literature. Using matrix-analytic methods we analyze MAP/M/c-type retrial queueing models along with Poisson signals in steady-state. Illustrative numerical examples including a comparison with previously published retrial queues are presented and they show marked improvements in providing a quality of service to the customers.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.89-94
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• 2001

There are many queueing systems where customers wait for service up to a certain amount of time and leave the system if they are not served during that time. This paper considers a finite capacity multi-server queueing system with Poisson input and Erlang service time, where a customer becomes a lost customer when his service has not begun within an exponential patient time after his arrival. Performance measures such as average queue length, the average number of customers in service, and the proportion of lost customers can be obtained exactly through the proposed numerical solution procedure.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.95-102
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• 2016

Multi-server queueing systems with retrials are widely used to model problems in a call center. We present an explicit formula for an approximation of the queue length distribution in a multi-server retrial queue, by using the Lerch transcendent. Accuracy of our approximation is shown in the numerical examples.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.25 no.5
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• pp.31-38
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• 2002

In this paper, we model a two-server queueing system with priority, to which we put a restriction on the number of servers for each customer class. customers are divided into two different classes. Class 1 customers have non-preemptive priority over class 2 customers. They are served by both servers when available but class 2 customers are served only by a designated server. We use a method of generating function depending on the state of servers. We find the generating function of the number of customers in queue, server utilization, mean queue length and mean waiting time for each class of customers.

• Journal of Korean Institute of Industrial Engineers
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• v.42 no.1
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• pp.30-37
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• 2016

A multi-server queueing system with an infinite buffer and impatient customers is analyzed. The system operates in the finite state Markovian random environment. The number of available servers, the parameters of the batch Markovian arrival process, the rate of customers' service, and the impatience intensity depend on the current state of the random environment and immediately change their values at the moments of jumps of the random environment. Dynamics of the system is described by the multi-dimensional asymptotically quasi-Toeplitz Markov chain. The ergodicity condition is derived. The main performance measures of the system are calculated. Numerical results are presented.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.77-87
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• 2015

Parallel lines are often used to increase production rate in many manufacturing systems where the main line splits into several lines in parallel, and after some operations, they merge into a main line again. Queueing networks with finite buffers have been widely used for modeling and analyzing manufacturing systems. This paper provides an approximation technique for multi-server two-stage networks with merge configuration and blocking which will be a building block for analysis of general manufacturing systems with parallel lines and merge configuration. The main idea of the method is to decompose the original system into subsystems that have two service stations with multiple servers, two buffers and external arrivals to the second stage are allowed. The subsystems are modeled by level dependent quasi-birth-and-death (LDQBD) process.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.61
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• pp.13-22
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• 2000

To apply the queueing network theory in evaluating performances of flexible manufacturing systems, it is generally assumed that the processing times are distributed exponentially. However, in FMS, processing times are usually deterministic. In this study the performance measures of FMS are approximated under the assumption that processing times are usually deterministic. Multi-classes of parts and single server and multi-server stations are considered in the model. This study also that, in the numerical example, this approach yields better solutions than those obtained by the pure Linearizer algorithm, when the processing times are deterministic.